Finite Group Databasebeta

← #14726892

Subgroups — #14726892

Order 2816.

1154 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078643C212yesmaximal, complemented
2#13073978C211yesmaximal, characteristic, complemented
3#13067653C214yesmaximal, complemented
4#13067585C214yesmaximal, complemented
5#13067176C212yesmaximal, complemented
6#13066940C211yesmaximal, characteristic, complemented
7C11×#3497C211yesmaximal, characteristic
8C2×C11×2−1+4—21no—
9C11×#550—22no—
10D4×Q8×C11—22no—
11C11×#548—24no—
12C11×#537—21no—
13C11×#537C2214yes—
14C11×#532—22no—
15C11×#532C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18#10622843—21no—
19#10622707—22no—
20#10622688—22no—
21#10622653C2214yes—
22#10622647C2214yes—
23C4×#4324—24no—
24#10622599C2212yes—
25#10622592C2212yes—
26#10622586—21no—
27#10622549C2211yescharacteristic
28#10622546—22no—
29#10622538C2212yes—
30#10622175C2218yes—
31#10622166C2214yes—
32C11×2−1+4—44no—
33C11×2−1+4—44no—
34C2×C11×#41—24no—
35C2×C11×#41—24no—
36C2×C11×#41—22no—
37C22×Q8×C11—24no—
38C22×Q8×C11D411yescharacteristic
39C22×Dic22C2311yescharacteristic
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8D412yes—
42C11×#127—22no—
43C11×#127D412yes—
44C11×#124—24no—
45C11×#124—22no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—28no—
48C11×#121—24no—
49C11×#121—28no—
50C11×#121—22no—
51C11×#121—24no—
52C11×#121C2314yes—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C4×D4×C11—24no—
56C4×D4×C11—24no—
57C4×D4×C11—22no—
58C4×D4×C11D414yes—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C42×C11D412yes—
62C2×C42×C11C2311yescharacteristic
63C2×#4324—24no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—21no—
67C2×Dic11⋊C4—22no—
68C2×C4×Dic11—21no—
69C4×Dic22—22no—
70C4×Dic22—22no—
71#66896—24no—
72C11⋊#95—21no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95C2312yes—
77C22⋊(C11⋊C8)C2314yes—
78#66874—24no—
79#66872—24no—
80C4⋊(C11⋊C8)—22no—
81C4×C11⋊C8—22no—
82#18219—111nomaximal, Sylow
83C11×#41—48no—
84C11×#41—416no—
85C11×#41—48no—
86C11×#41—44no—
87C11×#41—44no—
88C2×Q8×C11—24no—
89C2×Q8×C11—22no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11—416no—
93C2×Q8×C11SD1614yescomplemented
94C2×D4×C11—24no—
95C2×D4×C11—24no—
96C2×D4×C11—24no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11C2×D414yes—
100C22×C4×C11—28no—
101C22×C4×C11—24no—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—21no—
108C22×Dic11—22no—
109C22×Dic11—21no—
110C2×Dic22—22no—
111C2×Dic22—42no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4C2×D414yes—
117C11×C22⋊C4—28no—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—24no—
120C42×C11—22no—
121C42×C11—22no—
122C42×C11C2×D412yes—
123C42×C11C2×D412yes—
124#4324—48no—
125C4⋊Dic11—22no—
126C4⋊Dic11—42no—
127Dic11⋊C4—44no—
128Dic11⋊C4—41no—
129Dic11⋊C4—41no—
130C4×Dic11—42no—
131C2×C11⋊C8—24no—
132#3497D1111yescharacteristic
133#3103—112no—
134#2581—111no—
135#1616—114no—
136#1604—114no—
137#1517—112no—
138#1461—111no—
139C23×C11—24no—
140C23×C11C22×D411yescharacteristic
141Q8×C11—28no—
142Q8×C11—48no—
143Q8×C11—44no—
144D4×C11—44no—
145D4×C11—44no—
146D4×C11—48no—
147D4×C11—44no—
148D4×C11—44no—
149D4×C11—44no—
150D4×C11—84no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—24no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—416no—
158C2×C4×C11—48no—
159C2×C4×C11—42no—
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12012yes—
163C2×C4×C11C2×SD1614yes—
164C2×C4×C11C2×SD1612yes—
165C2×C4×C11AGL(1,ℤ/8)12yes—
166C2×C4×C11C22×D412yes—
167C2×Dic11—22no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—41no—
174C2×Dic11—42no—
175Dic22—24no—
176Dic22—42no—
177C11⋊C8—44no—
178C2×2−1+4—21no—
179#550—22no—
180D4×Q8—22no—
181#548—24no—
182#537—21no—
183#537C2×D1114yes—
184#532—22no—
185#532C2×D1112yes—
186C2×C4×Q8—111no—
187C2×C4×Q8C2×D1111yescharacteristic
188#481—114no—
189#475—222no—
190#460—222no—
191#448—114no—
192C4×SD16—224no—
193#431—112no—
194#400—112no—
195#395—112no—
196#391—221no—
197#389—221no—
198#387—222no—
199#382—111no—
200#327—118no—
201#324—114no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—44no—
205C22×C11—44no—
206C22×C11—44no—
207C22×C11C2×#12011yescharacteristic
208C22×C11C22×SD1611yescharacteristic
209C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
210C4×C11—24no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—22no—
214C4×C11—44no—
215C4×C11—42no—
216C4×C11#45014yes—
217Dic11—42no—
218Dic11—82no—
219Dic11—81no—
2202−1+4—44no—
2212−1+4—44no—
222C2×#41—24no—
223C2×#41—24no—
224C2×#41—22no—
225C22×Q8—24no—
226C22×Q8—111no—
227C22×Q8C22⋊D1111yescharacteristic
228C2×SD16—224no—
229C4⋊Q8—22no—
230C4⋊Q8C22⋊D1112yes—
231#127—22no—
232#127C22⋊D1112yes—
233#124—24no—
234#124—22no—
235C22⋊Q8—24no—
236C22⋊Q8—28no—
237#121—24no—
238#121—28no—
239#121—22no—
240#121—24no—
241#121C22×D1114yes—
242C4×Q8—22no—
243C4×Q8—22no—
244C4×Q8—222no—
245C4×Q8—222no—
246C4×D4—24no—
247C4×D4—24no—
248C4×D4—22no—
249C4×D4C22⋊D1114yes—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4—222no—
254C2×C4⋊C4C22⋊D1111yescharacteristic
255C2×C4⋊C4C22×D1112yes—
256C2×C42—221no—
257C2×C42C22⋊D1112yes—
258C2×C42C22×D1111yescharacteristic
259#106—224no—
260C4⋊C8—222no—
261#103—224no—
262#102—224no—
263C22⋊C8—114no—
264C4×C8—222no—
265#95—112no—
266#95—221no—
267#95—222no—
268#95—222no—
269#95—222no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—84no—
273C2×C11C2×#45011yescharacteristic
274C2×C11#302011yescharacteristic
275C2×C11#302511yescharacteristic
276#41—48no—
277#41—416no—
278#41—44no—
279#41—48no—
280#41—44no—
281C2×Q8—24no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—22no—
285C2×Q8—416no—
286C2×Q8—222no—
287C2×Q8—442no—
288C2×Q8#432414yescomplemented
289C2×D4—24no—
290C2×D4—24no—
291C2×D4—24no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4C2×C22⋊D1114yes—
295C22×C4—28no—
296C22×C4—24no—
297C22×C4—221no—
298C22×C4—222no—
299C22×C4—221no—
300C22×C4C2×C22⋊D1112yes—
301C22×C4C2×C22⋊D1112yes—
302C22×C4C2×C22⋊D1111yescharacteristic
303C22×C4C2×C22⋊D1111yescharacteristic
304C22×C4C23×D1111yescharacteristic
305SD16—448no—
306C2×C8—224no—
307C4⋊C4—24no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—24no—
311C4⋊C4—222no—
312C4⋊C4—444no—
313C4⋊C4—442no—
314C4⋊C4—441no—
315C4⋊C4—441no—
316C4⋊C4C2×C22⋊D1114yes—
317C22⋊C4—28no—
318C22⋊C4—24no—
319C22⋊C4—24no—
320C42—22no—
321C42—22no—
322C42—442no—
323C42C2×C22⋊D1112yes—
324C42C2×C22⋊D1112yes—
325C11#1821911yescharacteristic, complemented, Sylow
326C23—24no—
327C23C22×C22⋊D1111yescharacteristic
328Q8—28no—
329Q8—48no—
330Q8—44no—
331Q8—224no—
332Q8—442no—
333D4—44no—
334D4—44no—
335D4—48no—
336D4—44no—
337D4—44no—
338D4—44no—
339D4—84no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—24no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—416no—
347C2×C4—48no—
348C2×C4—42no—
349C2×C4—222no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4—441no—
357C2×C4#6698512yes—
358C2×C4C2×#432414yes—
359C2×C4C2×#432412yes—
360C2×C4#6700611yescharacteristic
361C2×C4#6700611yescharacteristic
362C2×C4#6700612yes—
363C2×C4C22×C22⋊D1112yes—
364C8—444no—
365C22—21no—
366C22—21no—
367C22—44no—
368C22—44no—
369C22—44no—
370C22C2×#6698511yescharacteristic
371C22C22×#432411yescharacteristic
372C22C2×#6700611yescharacteristic
373C4—24no—
374C4—21no—
375C4—21no—
376C4—22no—
377C4—44no—
378C4—42no—
379C4—442no—
380C4—882no—
381C4—881no—
382C4#1062283114yes—
383C2—21no—
384C2—21no—
385C2—84no—
386C2C2×#1062283111yescharacteristic
387C2#1307798011yescharacteristic
388C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3497C2
socleC22×C11C2×#120
hypercenter#3497D11
hypocenterC11#18219
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3497

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13078643C2semidirect
2. #13073978C2semidirect
3. #13067653C2semidirect
4. #13067585C2semidirect
5. #13067176C2semidirect
6. #13066940C2semidirect
93. C2×Q8×C11SD16semidirect
288. C2×Q8#4324semidirect
325. C11#18219semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130786432
#130739782
#130676532
#130675852
#130671762
#130669402
C11×#34972
#1821911